Variations in service delivery have been identified as a major challenge to the success of process improvement studies in service departments of hospital such as radiology. Largely, these variations are due to inherent system level factors, i.e., system variations such as unavailability of resources (nurse, bed, doctors, and equipment). These system variations are largely unnecessary/unwarranted and mostly lead to longer waiting times, delays, and lowered productivity of the service units. There is limited research on identifying system variations and modelling them for service improvements within hospital. Therefore, this paper proposes a modelling methodology to model system variations in radiology based on real time locating system (RTLS) tracking data. The methodology employs concepts from graph theory to identify and represent system variations. In particular, edge coloured directed multi-graphs (ECDMs) are used to model system variations which are reflected in paths adopted by staff, i.e., sequence of rooms/areas traversed while delivering services. The main steps of the methodology are: (i) identifying the most standard path followed by staff for service delivery; (ii) filtering the redundant events in RTLS tracking database for analysis; (iii) identifying rooms/areas of hospital site involved in the service delivery; (iv) determining patterns of paths adopted by staff from filtered tracking database; and, (v) representation of patterns in graph based model called as edge coloured directed multigraphs (ECDMs) of a role. A case study of MR scanning process is utilized to illustrate the implementation of the proposed methodology for modelling system variations reflected in the paths adopted by staff.